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Answer :
To find the weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, we need to multiply the weight of one particle by the total number of particles.
Here's the step-by-step calculation:
1. Weight of One Dust Particle:
[tex]\[
7.42 \times 10^{-10} \text{ kilograms}
\][/tex]
2. Number of Dust Particles:
[tex]\[
5 \times 10^6
\][/tex]
3. Total Weight Calculation:
- Multiply the weight of one dust particle by the number of particles:
[tex]\[
7.42 \times 10^{-10} \times 5 \times 10^6
\][/tex]
4. Breaking Down the Multiplication:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Then, handle the powers of ten: [tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
- Combine these results:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
Thus, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles is represented in scientific notation as:
[tex]\[
37.1 \times 10^{-4} \text{ kilograms}
\][/tex]
So, the correct answer is option D: [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
Here's the step-by-step calculation:
1. Weight of One Dust Particle:
[tex]\[
7.42 \times 10^{-10} \text{ kilograms}
\][/tex]
2. Number of Dust Particles:
[tex]\[
5 \times 10^6
\][/tex]
3. Total Weight Calculation:
- Multiply the weight of one dust particle by the number of particles:
[tex]\[
7.42 \times 10^{-10} \times 5 \times 10^6
\][/tex]
4. Breaking Down the Multiplication:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Then, handle the powers of ten: [tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
- Combine these results:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
Thus, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles is represented in scientific notation as:
[tex]\[
37.1 \times 10^{-4} \text{ kilograms}
\][/tex]
So, the correct answer is option D: [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
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